document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39858>Question 39858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My friend and I are trying to see who has the right answer to some problems. Could you please explain to us how to solve them the right way.\r<BR>\n" );
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document.write( "a. The monthly revenue achieved by selling x boxes of candy is calculated to be $ x(5-0.05x). The wholesale cost of each box of candy is $1.50.<BR>\n" );
document.write( "How many boxes must be sold each month to maximize profit?<BR>\n" );
document.write( "What is the maximum profit?<BR>\n" );
document.write( "(Revenue=Cost+Profit)\r<BR>\n" );
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document.write( "b. Bob has 3000ft of fencing available to enclose a rectangular field.<BR>\n" );
document.write( "1. Express the area A of rectangle as a function of x where x is the length of rectangle.<BR>\n" );
document.write( "2. For what value of x is the area largest?<BR>\n" );
document.write( "3.What is the maximum area?\r<BR>\n" );
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document.write( "Thank you so much! Now we will see who is right:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26407 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The total profit by selling 'x' boxes of candies is <BR>\n" );
document.write( "P = $(x(5-0.05x) - 1.5x) = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.5x+-+0.05x%5E2%29 ALIGN=MIDDLE  ALT=\"%283.5x+-+0.05x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For maximizing 'P', <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dP%2Fdx+=+0 ALIGN=MIDDLE  ALT=\"dP%2Fdx+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2P%2Fdx%5E2+%3C+0 ALIGN=MIDDLE  ALT=\"d%5E2P%2Fdx%5E2+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dp%2Fdx+=+0+=+3.5+-+2%2A0.05%2Ax+=+3.5+-+0.1x ALIGN=MIDDLE  ALT=\"dp%2Fdx+=+0+=+3.5+-+2%2A0.05%2Ax+=+3.5+-+0.1x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or x = 35<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2p%2Fdx%5E2+=++-+2%2A0.05+=+-0.1 ALIGN=MIDDLE  ALT=\"d%5E2p%2Fdx%5E2+=++-+2%2A0.05+=+-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thus P is maximum for x = 35 and corresponding P = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.5%2A35+-+0.05%2A35%5E2%29 ALIGN=MIDDLE  ALT=\"%283.5%2A35+-+0.05%2A35%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $61.25.<BR>\n" );
document.write( "So for maximum profit, 35 boxes are to be sold and the maximum profit is $61.25.\r<BR>\n" );
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document.write( "2. Perimeter = 3000 ft.<BR>\n" );
document.write( "Let length = L ft, width = W ft of the rectangular field.<BR>\n" );
document.write( "Then, 2(L + W) = 3000 or L + W = 1500 _________(1)<BR>\n" );
document.write( "Given: L = x, then from (1) W = 1500 - x.<BR>\n" );
document.write( "Hence, area A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2AW+=+x%2A%281500-x%29 ALIGN=MIDDLE  ALT=\"L%2AW+=+x%2A%281500-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sq ft<BR>\n" );
document.write( "To find maximum area, maximize A w.r.t x as done in the problem above.<BR>\n" );
document.write( "Then you get, x = 750 for maximum A and this maximum value of A is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2A750 ALIGN=MIDDLE  ALT=\"750%2A750\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 562500<BR>\n" );
document.write( "Hence area of the rectangular field is maximum when its each side is 750 ft i.e. the field is a square with side 750 ft and this maximum area enclosed is 562500 sq ft.\r<BR>\n" );
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document.write( "[V.V.I.: From this problem we come to the conclusion that of all rectangles with same perimeter, the square has the largest area.] </SPAN>\n" );
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